Curriculum / Math / 8th Grade / Unit 2: Solving One-Variable Equations / Lesson 12

Solving One-Variable Equations

Lesson 12

Math

Unit 2

8th Grade

Lesson 12 of 12

Objective

Solve and graph inequalities with variables on both sides of the inequality (optional).

Common Core Standards

Core Standards

The core standards covered in this lesson

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Reasoning with Equations and Inequalities

A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

The foundational standards covered in this lesson

7.EE.B.4.B

Expressions and Equations

7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Solve inequalities with variables on both sides and use substitution to check answers.
Accurately multiply and divide with negative coefficients in inequalities, paying close attention to the direction of the inequality symbol.
Graph solutions to inequalities.
Write, solve, and interpret solutions to inequalities for applications.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

25-30 minutes

Problem 1

Solve the inequality. Then pick a value for $$x$$ and check your answer. Lastly, graph your solution on a number line.

$$7-{2\over3}x>2+x$$

Guiding Questions

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Student Response

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Problem 2

Solve the inequality.

$${\frac{x-7}{3}\leq \frac{2(x-1)}{8}}$$

Guiding Questions

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Student Response

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Problem 3

Lindsay and Kiana work at the same restaurant. Lindsay earns $12.75 per hour and Kiana, who has been working there longer, earns $15.25 per hour. One week, both girls work the same number of hours at the restaurant, but Lindsay spends $37 and Kiana spends $55. At the end of the week, Lindsay has more money left than Kiana. What is the greatest number of hours the girls could have worked for this to be true?

Guiding Questions

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Student Response

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

5-10 minutes

Solve the inequality.

$${\frac{-2x+1}{4}< \frac{3x-6}{6}}$$

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems that cover all types of equations and inequalities.
Include application problems that cover all types of equations and inequalities; students determine if an equation or inequality best represents the situation.

Kuta Software Free Algebra 1 Worksheets Inequalities — Multi-Step Inequalities (Use inequalities with variables on both sides.)
Kuta Software Free Pre-Algebra Worksheets Inequalities — Multi-Step Inequalities (Use inequalities with variables on both sides.)

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Solving One-Variable Equations

Objective

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Common Core Standards

Core Standards

Reasoning with Equations and Inequalities

Foundational Standards

Expressions and Equations

Criteria for Success

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Tips for Teachers

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Anchor Problems

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Problem 1

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Guiding Questions

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Problem 2

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Guiding Questions

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Problem 3

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Guiding Questions

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Problem Set

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Target Task

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Additional Practice

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